Range of , where denotes greatest integer function,…

MATHEMATICS · Single correct · AoPS · Mathematics · Special Functions · Special Functions

Problem

Range of

f(x) = \left[ \frac{1}{\log(x^2 + e)} \right] + \frac{1}{\sqrt{1+x^2}}

, where

[ \cdot ]

denotes greatest integer function, is (1)

\left(0, \frac{e+1}{e}\right] \cup \{2\}

(2)

(0, 1)

(3)

(0, 1] \cup \{2\}

(4)

[0, 1] \cup \{2\}